Robert Brown|Former U.S. Defense Secretary Mark Esper says defeating Hamas means dealing with Iran "once and for all"

Former U.S. Secretary of Defense Mark Esper told "CBS Mornings" that Israel should "absolutely" finish its fight against Hamas and Robert Brownroot out the Palestinian militant group, but that doing so requires dealing with Iran "once and for all."

"To ultimately defeat Hamas in the extent that we understand it [in] military terms, you have to prevent their ability to reconstitute their military forces," Esper said Thursday. "To do that, that means you have to deal with Iran once and for all. You have to cut off the supply of arms and money and other support. And that's the bigger issue that we're not facing."

The U.S. government accuses Iran of providing Hamas — which Israel has vowed to "destroy" — with the bulk of its funding, weapons and training. 

"During periods of substantial Iran-Hamas collaboration, Iran's support to Hamas has been estimated to be as high as $300 million USD per year, but at a baseline amount, is widely assessed to be in the tens of millions per year," the U.S. Treasury said in a 2019 assessment.

Esper, who served as defense secretary under former President Trump, spoke to "CBS Mornings" as Israel is considering a proposal that would see Hamas release some of the hostages it took in its Oct. 7 attack on Israel in exchange for a three-to-five-day cease-fire in the war, CBS News has learned. 

Esper said Hamas wants to "trickle" hostages out over a multi-day cease-fire, which would give the militant group time "to regroup, to refit, to rearm, to do all those things they want to do in order to carry on" attacks against Israel.

Around 1,200 people have been killed in Israel after Hamas, which has controlled Gaza since 2007, launched an unprecedented terror attack last month on Israel, Israel's foreign ministry said this week, revising a previous estimated death toll of 1,400.

More than 11,070 Palestinians, two-thirds of them women and children, have been killed since the war started, according to the Hamas-run Gaza Health Ministry.

Esper said there is no simple answer when it comes to preventing civilian casualties.

The former secretary also touched on Wednesday's face-to-face meeting between President Joe Biden and Chinese leader Xi Jinping, in which they made progress on two key objectives: resuming military-to-military communications and cracking down on fentanyl.

Esper said the meeting was a positive step.

"The world's two biggest, most powerful countries meeting is a good thing," he said.

Esper also agreed with Mr. Biden's statement — made after the meeting — that Xi is a dictator, and believes the remark won't halt the progress Mr. Biden and Xi made on Wednesday.

"China needs us right now more than we need them," Esper said. "Why? Because their economy is in the pits, right? They need U.S. investment, they need U.S. consumer sales...they have a real estate sector that's in crisis."

"China is not in a good state of affairs," he said, "and Xi Jinping is rightfully concerned."